Modified Gaussian pseudo-copula: Applications in insurance and finance

- The Gaussian copula is modified to consider both tailed and elliptical dependence.
- Modified Gaussian copula is more versatile than Gaussian and Archimedean copula.
- Modified Gaussian copula maintain close-form conciseness while extending flexibility.
- We show modified Gaussian copula work well with real-life insurance and finance data.
- Modified Gaussian pseudo-copula can be extended straightforward to the multivariate case.

The Gaussian copula is by far the most popular copula for modeling the association in finance and insurance risk problems. However, one major drawback of Gaussian copula is that it intrinsically lacks the flexibility of modeling the tail dependence, which real life data often exhibit. In this paper, we present the modified Gaussian copula, a pseudo-copula model that allows for both tail dependence and elliptical dependence structure. To improve model flexibility, the Gaussian copula is modified such that each correlation coefficient is not only an unknown parameter (to be modeled), but also a function of random variables. We present the characteristics of the modified Gaussian pseudo-copula and show that our modification enables the copula to capture the tail dependence adequately. The proposed modified Gaussian pseudo-copula is assessed by estimating the association on a real life insurance data and a finance data set. Furthermore, a comprehensive simulation study comparing goodness-of-fit test statistics is carried out. Both experiment results demonstrate that our Modified Gaussian pseudo-copula fits data (with or without tail dependence) generally better than other common copulas.